curve #2621

y² + xy = x³ − 29909607691690x + 62959917901032424100

a-invariants: [1, 0, 0, -29909607691690, 62959917901032424100]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1113759570
discriminant (Δ): 144674091896571358535440502784000000
Faltings height: 6.2226
naive height: 104.7012
primes of bad reduction: 2, 3, 5, 7, 11, 37, 83, 157
regulator: 14.5964505019525371634419175649031769577419
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:16 UTC
last updated: 2026-09-26 20:13:16 UTC

Witness: 2 independent points log in to add more points →

(3152270, 14463770)
(3156596, 713222)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=40; A=(3q-p)(p+q)^3=4239, B=-(p+3q)(p-q)^3=37892239. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 20:13:16 UTC · history